Question

this cylinder has a volume of 405π cubic meters. what is its height? 9 m blank meters

Explanation:

Step1: Write the formula for the volume of a cylinder

The volume formula of a cylinder is \( V=\pi r^{2}h\), where \(V\) is the volume, \(r\) is the radius, and \(h\) is the height.

Step2: Substitute the given values into the formula

Given \(V = 405\pi\) and \(r=9\). Substitute into \(V=\pi r^{2}h\), we get \(405\pi=\pi\times9^{2}\times h\).

Step3: Simplify the equation

Divide both sides of the equation \(405\pi=\pi\times81\times h\) by \(\pi\). The equation becomes \(405 = 81h\).

Step4: Solve for \(h\)

Divide both sides of \(405 = 81h\) by 81. So \(h=\frac{405}{81}=5\).

Answer:

\(5\)